Mostly because England, Britain (or Great Britain), and the United Kingdom (UK) are all different things and are not synonymous. It's similar to saying California, the Continental US, and the USA are all the same thing and using them as synonyms.
England is a country that shares the island known as Great Britain, the largest island in the British Isles, with the two other countries of Wales and Scotland. While England and Wales tend to be more connected and Wales holds forty seats in the UK House of Commons, it does have its own parliament as well, the Senedd Cymru. Likewise, Scotland holds fifty-nine seats in the UK Parliament but also has an independent parliament of its own.
Britain is the name for the three countries on the island of Great Britain as a whole, and Britain and Great Britain are generally synonymous, though technically Britain contains the various smaller islands that are a part of England, Wales, and Scotland, while Great Britain when taken pedantically as just the island, does not (Note here that most uses of Great Britain refer to all of Britain including all small islands with the exception of the Isle of Man which is its own thing and not a part of the UK or Great Britain, though is a sort of protectorate...)
The United Kingdom also includes Northern Ireland or Ulster which from 1998 to 2017 had its own Assembly, which after collapsing in Jan of 2017 has been restored as of Jan 2020. It also has three seats in the UK Parliament. Hence its full name of "The United Kingdom of Great Britain and Northern Ireland." What a mouthful...
Interestingly, England is the only country in the UK that does not have a separate Assembly or Parliament outside of the Westminster UK Parliament and has not had one since the last English Parliament officially merged with the then Scottish Parliament to form the Westminster Parliament of Great Britain in 1707
Okay, history lesson part over.
Why it matters. Because you are talking about different entities. When you say "England should pay," this is different from saying "Britain should pay" or "The UK should pay." It would be like saying that "Mississippi should pay," is the same as "The South should pay," is the same as the "US Federal Government should pay."
In fact when you say "England" should pay, then what does that mean because England has no parliament as such anymore, but just representatives in the UK one.
When you say that "Britain should pay" well again, what does that mean? Because the Parliament of Great Britain hasn't existed since 1801 when Ireland joined it to become the Parliament of Great Britain and Ireland. Of course that no longer exists either with the Irish Free State, to become Eire or Ireland, and now the Republic of Ireland, splitting off in 1922, leaving the current UK Parliament. Should Northern Ireland have to help pay when it wasn't even a part of the Parliament of Great Britain in 1776?
It was suggested that it fall on the crown, but then there is the issue that the House, House Hanover, who held the Crown in 1776 ended with the death of William IV on 26th June 1830. Should the current House, House Winsor, be responsible for another House's actions just because they inherited the Crown? The suggestion is that the USA shouldn't inherit the debts of the Thirteen Colonies as they were under British sovereignty, but couldn't the same argument be played out with the Crown?
So yes, being clear about these things and not using them all to mean the same thing does have ramifications for different groups of people and is important, especially if it was to actually be more than a suggestion but something that was to have a legitimate and legal force behind it.